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On the Origin of Power-Law Fluctuations in Stock Prices

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  • Vasiliki Plerou
  • Parameswaran Gopikrishnan
  • Xavier Gabaix
  • H. Eugene Stanley

Abstract

We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large orders and potential autocorrelations in the trade flow. Our new analysis shows clearly that price impact and volume are related by a square-root functional form of market impact for large volumes, in contrast to the claim of FL that this relationship increases as a power law with a smaller exponent. Since large orders are usually executed by splitting into smaller size trades, procedures used by FL give a downward bias for this power law exponent. Second, FL analyze 3 stocks traded on the London Stock Exchange, and solely on this basis they claim that the distribution of transaction volumes do not have a power-law tail for the London Stock Exchange. We perform new empirical analysis on transaction data for the 262 largest stocks listed in the London Stock Exchange, and find that the distribution of volume decays as a power-law with an exponent $\approx 3/2$ -- in sharp contrast to FL's claim that the distribution of transaction volume does not have a power-law tail. Our exponent estimate of $\approx 3/2$ is consistent with our previous results from the New York and Paris Stock Exchanges. We conclude that the available empirical evidence is consistent with our hypothesis on the origin of power-law fluctuations in stock prices.

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File URL: http://arxiv.org/pdf/cond-mat/0403067
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0403067.

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Date of creation: Mar 2004
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Publication status: Published in Quantitative Finance 4 (February 2004) C11-C15
Handle: RePEc:arx:papers:cond-mat/0403067

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Web page: http://arxiv.org/

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Cited by:
  1. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
  2. Chiarella, C. & Iori, G. & Perello, J., 2008. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Working Papers 08/04, Department of Economics, City University London.
  3. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
  4. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156, arXiv.org, revised May 2006.
  5. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
  6. Kang, Sang Hoon & Yoon, Seong-Min, 2008. "Long memory features in the high frequency data of the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5189-5196.
  7. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
  8. J. -P. Bouchaud & J. Kockelkoren & M. Potters, 2004. "Random walks, liquidity molasses and critical response in financial markets," Papers cond-mat/0406224, arXiv.org, revised Jun 2004.
  9. Kostanjcar, Zvonko & Jeren, Branko & Juretic, Zeljan, 2012. "Impact of uncertainty in expected return estimation on stock price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5563-5571.
  10. Wei-Xing Zhou, 2007. "Universal price impact functions of individual trades in an order-driven market," Papers 0708.3198, arXiv.org, revised Apr 2008.
  11. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H., 2008. "Quantifying and understanding the economics of large financial movements," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 303-319, January.
  12. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  13. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, Eugene, 2007. "A unified econophysics explanation for the power-law exponents of stock market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 81-88.

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